If f(x) is a function with period 2L = 4 given on the interval (−2, 2) with (in the picture) (a) Expansion f(x) using the Fourier series. (b) Using the Fourier series in (c), prove that (in the picture)
Q: Find the expected ualue of the Harmonic oscillator function Un lx) =Nexp ( *z) Hn Lx)
A: it is required to find the expected value of the given harmonic oscillator function. Here the given…
Q: uonenba x(k + 2) + 3x(k + 1) + 2r(k) = e(k) %3D where k = 0 otherwise 1, e(k) = %3D 0, x(0) = 1 %3!…
A:
Q: (a) Using the matrix representations of Ŝ,, Šy, Š2, show that S., Ŝ, = -iħŜ„. (b) For two general…
A:
Q: (a) Find the Fourier series of the function f(x) = x²,0 ≤ x < L with period L. (b) Use the previous…
A: Given:
Q: (a) Show that the transformation Q = p + iaq, P = (p − iaq) / (2ia) is canonical and find a…
A:
Q: Verify that the operator in momentum representation is given by use the methods shown in class by…
A:
Q: Find the fourier transform of f(x) defined by f(x) = { = ( and hence evaluate +∞ sin pacos pl du |x|
A:
Q: S₁√ B. ds =
A:
Q: Find the Z Transform for the following function: f(t)=e^(-ct) cos(2πt/3)u(t)
A: To find the Z-transform of the given function, we can first write the function in terms of the…
Q: Normalize the wave function e-(2r/b) sin sin over the interval 0 ≤r <∞,0 ≤ 0 ≤ T, 0≤ ≤ 2π. The…
A: To normalize wave function, we integrate the square of wave function. So when we integrate over…
Q: (4) When variables p, V,T are related by F(p,V,T) = 0, show the following relations (see any…
A: Given that The function is fp,V,T=0 To prove a) ∂p∂TV=1∂T∂pV b) ∂p∂TV+∂p∂VT∂V∂Tp=0 c)…
Q: In a region of space there exists a uniform electrostatic field E, of given direction and direction.…
A: Given that electric field is uniform. The potential is given by dU=-E.dx If E is uniform then after…
Q: The point P(25, 9) lies on the curve y = secant line PQ for the following values of x. VI + 4. If Q…
A: slope is given by, m = ∆y∆x a) if x = 25.1 y=f(25.1) =9.0099 slope = 9.009-9.00025.1-25m = 0.09 b)…
Q: lielectric constant, index of refraction and absorption coefficient for a non-conducting medium
A:
Q: The graph of a real periodic function f (x) for the range [-00, co] is shown below fx) AAA Which of…
A:
Q: A particle of mass m moves inside a potential energy landscape U (2) = X|2| along the z axis. Part…
A: To determine the units of the constant λ, we can use the given formula for potential energy U(z) and…
Q: Obtain Fourier transformation for following function and also its integral representations.
A:
Q: The translation operator for a finite spatial displacement is given in several dimensions by T(l) =…
A: Solution: Given Operator: T^(l)=exp-2πiplh
Q: The Fourier transform of a function f (x) is defined as: f (w) = L dx f (ω) -. f (x)e-iwx Similarly,…
A: Given, Fourier transform formula and inverse Fourier transform formula And the function f(x) .
Q: 2) Consider a particle in a three-dimensional harmonic oscillator potential V (x, y, 2) = ;mw (x² +…
A: Let the given particle is the electron. Then the transition probability (W) be given as, Where, ω…
Q: Find the Fourier transform of rect(t/4). (a) sinc(w) (b) sinc(w) (c) sinc(2w) (d) 2 sinc(2w)
A:
Q: Consider the similarity transform of a matrix a to A’ given A’ = S-1AS. You need to prove | A n | =…
A: as A'=S-1AStherefore1. (A')n=S-1ASS-1ASS-1AS...........S-1AS where the term in square…
Q: Q.1 (a) Sketch signal h(t) which is defined by: h(t) = -28(t + 1) + 5u(t + 1) - 2u(t) - 5u(t – 1) +…
A:
Q: Given [yth, y²] + = 27¹², i 2 [μ²] = 0μv where is the mostly positive Minkowski metric and are the…
A:
Q: Consider the two planes (5x+y-z=0) and (x-2y+3z=-1) Argue why the intersection of these two planes…
A: Intersection of two planes:
Q: f(x, y) = (cos(x) + cos(yV3/2 – a/2) + cos(yv3/2+x/2))² Plot the contours of this function for -3…
A: A contour plot is a graphical method to visualize the 3-D surface by plotting constant Z slices…
Q: Let X be a random variable whose density is given by the formula f(x) = cx2 if x ∈ (0, 2)…
A: Given: The density is given by, f(x)=cx2 if x∈0,20 if otherwise Introduction: A random variable is…
Q: Prove that the expression e*/(1+ e*)² is an even function of x.
A:
Q: (2) The natural independent variables for U are (S,V), from dU = Tds - pdV. U = U (S,V) gives simple…
A: The first law of thermodynamics is
Q: Calculate the period of oscillation of ?(x,t) for a particle of mass 1.67 × 10-27 kg in the first…
A: This question can be solved by using quantum mechanical equation.potential well formula
Q: Find the Fourier Series corresponding to the f(x) define over interval (-2,2) as follows f(x) = 2…
A: The function fx is defined over the interval -2,2 Now, fx=2, -2≤x≤0x, 0≤x≤2 We know, Fourier…
Q: Consider a periodic signal x(t) with period T defined as follows: T (5t, - / < t <0 x(t) = T 10,…
A:
Q: Use a proof by contradiction to show that for all integers n, n²- 2 is not divisible by 4.
A: Introduction: Suppose the given function n2-2 is divisible by 4 then we can check whether it is…
Q: (c) At any time t, a particle is represented by the wavefunction w(x,1)= AeMe-lan where 2 and o are…
A:
Q: A cylinder (round can) has a circular base and a circular top with vertical sides in between. Let r…
A: Given: The radius of the cylinder is r. The height of the cylinder is h. The total surface area of…
Q: It is impossible within a finite amount of time to add an infinitely- numerous series of terms…
A:
Q: Using partial derivatives, calculate the propagated uncertainty in the mass in the following case:…
A: Given that, centripetal force Fc = (20.0 ± 0.5) N, angular velocity w = (29.2 ± 0.3) rad/s, radius R…
Q: 16. What is the decay rate of carbon 147 Express your answer in yr. 17. In dating using radiocarbon,…
A: Solution: 16. The decay rate is given in terms of half-life of radioactive material is given by,…
If f(x) is a function with period 2L = 4 given on the interval (−2, 2) with (in the picture)
(a) Expansion f(x) using the Fourier series.
(b) Using the Fourier series in (c), prove that (in the picture)
Step by step
Solved in 2 steps